How do I set up a driver to drive a node value with a node group input?
The best way is to completely avoid drivers inside node groups. They do not update correctly and are only trouble.

You should make your own custom Rotate node with the angle value accessible. You can make almost any spacial transformation using the correct math put together with Math nodes. Rotating a 3d vector around Z axis θ degrees looks like this:

x' = x cos θ − y sin θ 
y' = x sin θ + y cos θ 
z' = z


In nodes it looks like this:



The white node is there to convert degrees into radians.

If you really need you can build your own Mapping node with translation, rotation and scale inputs exposed.